Triply Periodic Minimal Surfaces - Disphenoid Surfaces

Note: What is referred to below as a "unit cell" is a unit cell for the
unoriented surface; the oriented unit cell is twice as big.

Schwartz' D surface - genus 3

At left is four fundamental regions in a disphenoid, with two C2 axes.
At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic
unit cell formed from four cubelets. At right is a rhombic dodecahedron made
of 24 disphenoids.
Evolver file: dcell.fe

Family A

This family progressively introduces a new edge along the long side of
the disphenoid.

Schoen's complementary D surface - genus 19

At left is four fundamental regions in a disphenoid, with two C2 axes.
At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic
unit cell formed from four cubelets. At right is a rhombic dodecahedron made
of 24 disphenoids.
Evolver file: disphenoid19.fe

New disphenoid surface - genus 31

At left is four fundamental regions in a disphenoid, with two C2 axes.
At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic
unit cell formed from four cubelets. At right is a rhombic dodecahedron made
of 24 disphenoids.
Evolver file: disphenoid31adj.fe

New disphenoid surface - genus 43

The next member in the family of the previous surface.
At left is four fundamental regions in a disphenoid, with two C2 axes.
At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic
unit cell formed from four cubelets. At right is a rhombic dodecahedron made
of 24 disphenoids.
Evolver file: disphenoid43adj.fe

New disphenoid surface - genus 55

The next member in the family of the previous surface.
At left is four fundamental regions in a disphenoid, with two C2 axes.
At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic
unit cell formed from four cubelets. At right is a rhombic dodecahedron made
of 24 disphenoids.
Evolver file: disphenoid55adj.fe

Family B

This family progressively introduces a new edge along the short side of
the disphenoid.

Schoen's complementary D surface - genus 19

At left is four fundamental regions in a disphenoid, with two C2 axes.
At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic
unit cell formed from four cubelets. At right is a rhombic dodecahedron made
of 24 disphenoids.
Evolver file: disphenoid19.fe

New disphenoid surface - genus 35

At left is four fundamental regions in a disphenoid, with two C2 axes.
At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic
unit cell formed from four cubelets. At right is a rhombic dodecahedron made
of 24 disphenoids.
Evolver file: disphenoid35adj.fe

New disphenoid surface - genus 51

At left is four fundamental regions in a disphenoid, with two C2 axes.
At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic
unit cell formed from four cubelets. At right is a rhombic dodecahedron made
of 24 disphenoids.
Evolver file: disphenoid51adj.fe